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lim(x->2)((x^5-32)/(x^3-8))...

`lim_(x->2)((x^5-32)/(x^3-8))`

Text Solution

Verified by Experts

`lim_(xto2)((x^(5)-32)/(x^(3)-8))=lim_(xto2) ((x^(5)-2^(5))/(x^(3)-2^(3)))`
`=lim_(xto2){((x^(5)-2^(5))/(x-2))-:((x^(3)-2^(3))/(x-2))}`
`=lim_(xto2)((x^(5)-2^(5))/(x-2)) -: lim_(xto2)((x^(3)-2^(3))/(x-2))`
`=[(5xx1^(4))-:(3xx2^(2))] " " [ :' lim_(xtoa)((x^(n)-a^(n))/(x-a))=na^(n-1)]`
`=(80/12)=20/3.`
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